Superconducting circuits are among the leading platforms for quantum computing. The main building block of a superconducting circuit is the superconducting qubit, which is based on the Josephson tunnel junction, a non-dissipative and non-linear electrical element that enables long-coherence times and high-fidelity gate operations. With recent advances in scaling to qubit arrays and surface code architectures, significant efforts are being made to reduce errors due to unintentional cross-talk between qubits and to avoid leakage into non-computational states.
The past years have shown rapid progress towards the realization of a topological superconductor (TSC), which is a quasi one-dimensional superconductor that hosts Majorana bound states (MBSs) at its ends and which may be useful in building a robust quantum computer. (An MBS is a zero-energy quasi-particle in a superconductor. An MBS is its own anti-particle.) Potential platforms for TSCs include hybrid superconductor (SC)-semiconductor nanowire devices under magnetic fields, chains of magnetic atoms on top of a SC substrate, and vortices in SC-topological insulator heterostructures. These platforms are designed to search for unpaired MBSs.
Topological superconductivity may also exist in time-reversal-invariant (TRI) systems (systems that are not exposed to magnetic fields) and could give rise to Kramers doublets of MBSs, also called Majorana Kramers pairs (MKPs). (An MKP consists of exactly two MBSs that transform into each other through the time-reversal symmetry operation.) In particular, a one-dimensional TRI TSC wire could host spatially separated MKPs at its two ends. Despite consisting of two MBSs, an isolated MKP is a robust zero-energy degree of freedom protected by time reversal symmetry and is therefore time-reversal-invarient.